Problem: If we express $2x^2 + 6x + 11$ in the form $a(x - h)^2 + k$, then what is $h$?
Solution: We complete the square.  First, we factor 2 out of the terms $2x^2 + 6x$ to get $2(x^2 + 3x)$.  We can square $x + 3/2$ to get $x^2 + 3x + 9/4$, so $h = \boxed{-\frac{3}{2}}$.